The present invention relates to a process for preparing a functionalized diene elastomer, in particular a functionalized polybutadiene with a high level of cis-1,4 linkages that has both a high Mooney viscosity and a reduced polydispersity index. The process according to the invention comprises the reaction of a catalyst system with at least one conjugated diene monomer to be polymerized then the addition of a functionalizing agent to the polymer thus obtained, the catalyst system comprising: - optionally a preforming conjugated diene, - a salt of one or more rare earth metal(s), - an inert hydrocarbon-based solvent, - an alkylating agent and - a halogen donor with exclusion of alkylaluminium sesquihalides, said reaction being carried out at a polymerization temperature less than or equal to 30°C, preferably between 0°C and 25°C.